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Chapter 29: Problem 15

The fields of an electromagnetic wave are \(\vec{E}=E_{p} \sin (k z+\omega t) \hat{\jmath}\) and \(\vec{B}=B_{p} \sin (k z+\omega t) \hat{\imath} .\) Give a unit vector in the wave's propagation direction.

Short Answer

Expert verified
The unit vector in the wave's propagation direction is -\(\hat{k}\).

Step by step solution

01

Identify electric and magnetic fields equation

From the problem statement, the electric field \(\vec{E}\) is along the \(\hat{\jmath}\) direction and the magnetic field \(\vec{B}\) is along \(\hat{\imath}\) direction.
02

Apply right-hand rule

The right-hand rule can be applied in electromagnetics to find the direction of wave propagation. For this problem, the index finger represents the \(\vec{E}\) field direction (\(\hat{\jmath}\)), the middle finger represents the \(\vec{B}\) field direction (\(\hat{\imath}\)), and the thumb would represent the direction of propagation.
03

Determine the propagation direction

To solve for the propagation direction, you need to determine the cross product of the electric and magnetic fields vectors, which points in the direction of wave's propagation. The cross product of \(\hat{\jmath}\) and \(\hat{\imath}\) gives a third orthogonal direction, using the right hand rule, which is -\(\hat{k}\).

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